Question

Three famous singers Lady Gaga, Taylor Swift and Katy Perry invest some amount in a music concert. They shared the profit in a business in the ratio 5 ∶ 7 ∶ 8. But they had partnered for 14 months, 8 months and 7 months respectively. Calculate the ratio of  their investments?
1. 5 ∶ 7 ∶ 8
2. 13 ∶ 17 ∶ 18 
3. 38 ∶  28 ∶ 21
4. 20 ∶  49 ∶ 64

Answer 1

Correct Answer - Option 4 : 20 ∶  49 ∶ 64

Given∶

Ratio of their profit = 5 ∶ 7 ∶ 8.

They had partnered for 

14 months, 8 months and 7 months.

Formula Used∶

Basics of ratios.

Calculation∶

Lady Gaga's investment be $ for 14 months, Taylor investment $ y for 8 months and Katy invest $ z for 7 months respectively.

Then,

⇒ 14x ∶ 8y ∶ 7z = 5 ∶ 7 ∶ 8

⇒ 14x/8y = 5/7

⇒ 98x = 40y

⇒ y = 49x/20

And 14x/7z = 5/8

⇒ 112x = 35z

⇒ z = 112x/35 = 16x/5

Thus, Required ratio ⇒ x ∶ y ∶ z = x ∶ 49x/20 ∶ 16x/5 = 20 ∶ 49 ∶ 64

∴ The ratio of their investments is 20 ∶ 49 ∶ 64.